# Correct Notation of Radiation Pattern of an Antenna

I have a confusion regarding the notation of radiation pattern of an antenna array. Some literatures use, say, $$F(r,\theta,\phi)$$ to denote the same while others use $$F(\theta,\phi)$$I would appreciate if anyone tells me the proper notation for the same. I am writing a report and I am not sure which notation to follow to represent the radiation pattern(field/power).

• "r" is usually the distance from the antenna so not specifying "r" would seem pointless unless it's just for field measurements at the antenna really close up? – Andy aka Jan 4 '16 at 13:49
• Well I am dealing with radiation patterns at the far field and in majority of popular literature like Balanis, Thiele, etc. "r" is ignored in the notation of radiation pattern which is making me wonder "why is it ignored" and "which notation" to use in my report. – rmb Jan 4 '16 at 14:15
• Links to both literature pieces is likely required to answer this. – Andy aka Jan 4 '16 at 14:21
• Since the books are not available online, I am posting the online wiki link explaining radiation pattern. Here also "r" has been ignored. – rmb Jan 4 '16 at 16:43
• Just a tip, but unless there is a defined standard in your class/field, you need to specify whether $\theta$ and $\phi$ are bearing and azimuth or azimuth and bearing. Different math and engineering books exchange them and it can be super confusing. – Daniel Jan 5 '16 at 2:28

## 1 Answer

The inclusion of r makes it a near-field measurement. The far-field measurement is an approximation based on the assumption that r is approaching infinity, which in practise means that r is many times larger than the antenna.

If you care about near-field effects, then you must use the near-field form. If you don't care about near-field, i.e. if your antennas are spaced apart by at least a few tens of their size, then you should simplify your report by using only the far-field radiation patterns.

The near-field expression probably gives you a direct expression for field-strength or power at each (r, theta, phi) point in space, whereas the far-field expression usually just tells you the antenna gain with respect to isotropic (dBi) in each (phi, theta) direction. The way you use each expression therefore differs because one includes propagation loss and the other does not; you must account for 1/r^2 (= -20log(r) dB) propagation losses if you're using the far-field patterns to compute total power transfer between antennae.